# An Elastic Interaction-Based Loss Function for Medical Image Segmentation

arXiv: https://arxiv.org/abs/2007.02663 · HTML: https://mlsanity.com/paper/2007.02663/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2020.

## Built on by (most cited first, 9 of 9)

- [Study Group Learning: Improving Retinal Vessel Segmentation Trained with Noisy Labels](https://mlsanity.com/paper/2103.03451/) (2021)
- [Retinal Vessel Segmentation with Pixel-wise Adaptive Filters](https://mlsanity.com/paper/2202.01782/) (2022)
- [A Novel Hybrid Approach for Retinal Vessel Segmentation with Dynamic Long-Range Dependency and Multi-Scale Retinal Edge Fusion Enhancement](https://mlsanity.com/paper/2504.13553/) (2025)
- [GAEI-UNet: Global Attention and Elastic Interaction U-Net for Vessel Image Segmentation](https://mlsanity.com/paper/2308.08345/) (2023)
- [Uncertainty-aware retinal layer segmentation in OCT through probabilistic signed distance functions](https://mlsanity.com/paper/2412.04935/) (2024)
- [(M)SLAe-Net: Multi-Scale Multi-Level Attention embedded Network for Retinal Vessel Segmentation](https://mlsanity.com/paper/2109.02084/) (2021)
- [Elastic Interaction Energy-Informed Real-Time Traffic Scene Perception](https://mlsanity.com/paper/2310.01449/) (2023)
- [ElasticLaneNet: An Efficient Geometry-Flexible Approach for Lane Detection](https://mlsanity.com/paper/2312.10389/) (2023)
- [BSC-Net: A Small-Branch-Sensitive Structural Continuity Network for Coronary Vessel Segmentation and Quantitative Angiographic Analysis](https://mlsanity.com/paper/2609.15400/) (2026)

## Abstract (arXiv)

Deep learning techniques have shown their success in medical image segmentation since they are easy to manipulate and robust to various types of datasets. The commonly used loss functions in the deep segmentation task are pixel-wise loss functions. This results in a bottleneck for these models to achieve high precision for complicated structures in biomedical images. For example, the predicted small blood vessels in retinal images are often disconnected or even missed under the supervision of the pixel-wise losses. This paper addresses this problem by introducing a long-range elastic interaction-based training strategy. In this strategy, convolutional neural network (CNN) learns the target region under the guidance of the elastic interaction energy between the boundary of the predicted region and that of the actual object. Under the supervision of the proposed loss, the boundary of the predicted region is attracted strongly by the object boundary and tends to stay connected. Experimental results show that our method is able to achieve considerable improvements compared to commonly used pixel-wise loss functions (cross entropy and dice Loss) and other recent loss functions on three retinal vessel segmentation datasets, DRIVE, STARE and CHASEDB1.